Behavioral Modeling of Chaos-Based Applications by Using Verilog-A

In general, a system can be defined as a collection of interconnected components that transforms a set of inputs received from its environment to a set of outputs. From an engineering point of view, chaos-based applications can be classified as a electronic system where the vast majority of the internal signals used as interconnections are electrical signals. Inputs and outputs are also provided as electrical quantities, or converted from, or to, such signals using sensors or actuators. To gain insight about the overall performance of the particular chaos-based application, the whole system must be characterized and simulated simultaneously. That is not a trivial task because the complexity of each one of the blocks that comprises the system, as well as the intrinsic complex behavior of chaotic generators. In this chapter, a modeling strategy suited to represent chaos-based applications for different control parameters of chaotic systems is presented. Based on behavioral descriptions obtained from a Hardware Description Language (HDL), called Verilog-A, two applications of chaotic systems are analyzed and designed. More specifically, a chaotic sinusoidal pulse width modulator (SPWM) which is useful to develop control algorithms for motor drivers in electric vehicles, and a chaotic pulse position modulator (CPPM) widely used in communication systems are presented as cases under analysis. Those applications are coded in Verilog-A and by using different abstraction levels, the indications of the degree of detail specified on how the function is to be implemented are obtained. Therefore, these behavioral models try to capture as much circuit functionality as possible with far less implementation details than the device-level description of the electronic circuit. Several circuit simulations applying H-Spice simulator are presented to demonstrate the usefulness of the proposed models. In this manner, behavioral modeling can be a possible solution for the successful development of robust chaos-based applications due to various types of systems that can be represented and simulated by means of an abstract model.